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SUMMARY:Generalized Power Methods for Group Synchronization Problems
DTSTART:20230309T150000
DTEND:20230309T160000
DTSTAMP:20260406T222114Z
UID:59a60c4b239ee65544a55f420c153e24e6a7a9d3c957aff33eb5afb6
CATEGORIES:Conferences - Seminars
DESCRIPTION:Professor Man-Chung Yue\, University of Hong Kong\n\nBiography
 \nDr. Man-Chung Yue is currently an Assistant Professor at the Musketeers 
 Foundation Institute of Data Science and the Department of Industrial and 
 Manufacturing Systems Engineering\, The University of Hong Kong. He receiv
 ed his B.Sc. degree in Mathematics and Ph.D. degree in Systems Engineering
  and Engineering Management\, both from The Chinese University of Hong Kon
 g. Before joining The University of Hong Kong\, he worked in The Hong Kong
  Polytechnic University as an Assistant Professor and Imperial College Lon
 don as a Research Associate. His research focuses on continuous optimizati
 on and its interplay with decision-making under uncertainty\, signal proce
 ssing\, machine learning and operations research. \n \nAbstract\nGroup s
 ynchronization problems (GSPs) aim at recovering a collection of group ele
 ments based on their noisy pairwise comparisons and find a wide range of 
 applications in areas such as machine learning\, molecular biology\, robot
 ics and computer vision. Existing approaches to GSPs are designed only for
  a specific subgroup\, do not scale well and/or lack theoretical guarantee
 s. In this talk\, we present a unified approach to the important sub-class
  of GSPs associated with any closed subgroup of the orthogonal group\, whi
 ch consists of a suitable initialization and an iterative refinement step 
 based on the generalized power method. Theoretically\, we show that our ap
 proach enjoys a strong guarantee on the estimation error under certain con
 ditions on the group\, measurement graph\, noise and initialization. We al
 so show that the group condition is satisfied for the orthogonal group\, t
 he special orthogonal group\, the permutation group and the cyclic group\,
  which are all practically relevant subgroups of the orthogonal group. We 
 then verify the conditions on the measurement graph and noise for standard
  random graph and random matrix models. Finally\, based on the classical n
 otion of metric entropy\, we develop a novel spectral-type estimator for G
 SPs\, which can be used as the initialization of our approach.\n\n 
LOCATION:ODY 4 03 https://plan.epfl.ch/?room==ODY%204%2003
STATUS:CONFIRMED
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